The Torelli group of a closed oriented surface of genus is the subgroup of the mapping class group consisting of all mapping classes that act trivially on the homology of . One of the most intriguing open problems concerning Torelli groups is the question of whether the group is finitely presented. A possible approach to this problem relies on the study of the second homology group of using the spectral sequence for the action of on the complex of cycles. In this paper we obtain evidence for the conjecture that is not finitely generated and hence is not finitely presented. Namely, we prove that the term of the spectral sequence is not finitely generated, that is, the group remains infinitely generated after taking quotients by the images of the differentials and . Proving that it remains infinitely generated after taking the quotient by the image of would complete the proof that is not finitely presented.

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关于 Torelli 属群对循环复合体的作用的谱序列

封闭定向曲面的 Torelli 群 属 是子群 映射类组 由所有作用于同源性的映射类组成 . 关于 Torelli 群的最有趣的开放性问题之一是该群是否 是有限呈现的。解决这个问题的一种可能方法依赖于对第二同源群的研究 使用光谱序列 为了行动 关于循环的复数。在本文中，我们获得了以下猜想的证据 不是有限生成的，因此 不是有限地呈现的。即，我们证明了 的谱序列不是有限生成的，即群 通过微分图像取商后仍然无限生成 和 . 证明它在乘以图像的商后仍然是无限生成的 将完成证明 不是有限地呈现的。